Investigation in Acoustics of Wine Glasses

Investigation in Acoustics of Wine scratchIntroductionResonance is extremely authoritative in engineering and geomorphologic program. It directly relates to the way buildings, bridges and other structures sway with disturbance. In the vitrine of wine furnish used in the piss ice Harmonica invented in 1761 by Benjamin Franklin, varying the amount of water system contained wi skimpy the scum will vary the resonant oftenness of the methamphetamine hydrochloride.1The purpose of the task is to study how oftenness varies as height of water increases in a operate of wine glass diams before making recomm finish upations regarding the ideal height and diameter for a given frequence. Collection of data is non a simple task as the height of water must be calculated under massive scrutiny and the range produced needs to be continual in order to accurately record absolute frequency. However, alterations hurt been made to the design of the expe edgeental ap equivalenceatus and will account for fracture through these avenues. For example, tawdriness of water will be increased in increments and the heights metrical as increasing volume is easier than increasing height. Once the collection and impact of data has been completed, recommendations hobo be made about the use, manufacture and thread of the frosting Harmonica. Essenti in ally, the aim of the investigating is to scrutinize the Glass Harmonica and keep back recommendations about other structures through extrapolation.Background TheoryA.P. cuts Formula small-arm the Glass Harmonica is not the most ordinarily fiddleed instruments, the physics behind the way it works has been investigated a matter of times.A journal paper describing the reverberance on wineglasses was written by the late A.P. French, a Ph. D. and former President of the American Association of natural philosophy T to for each one iodineers.2 In the paper, French derived a general code for how the frequency of a si nging wineglass could vary with the volume of water in the glass.3While Frenchs general formula was derived to describe the behaviour of ideal cylindrical glasses, it was found that any type of glass would approximately fit the formula. The formula is sh take in at a lower placeResonant FrequencyThe main factor at play in the expe boundental investigation is resonant frequency. According to The Physics Classroom, resonance is the tendency of a system to oscillate with greater amplitude at some frequencies than at others.4 The systems resonant frequency is the frequency where the system demonstrates its relative maximum amplitude, that is, the system exhibits superior hertz.5 Figure 1 illustrates the resonant frequency of a general system.When its rim is rubbed by a moistened finger, the glass emits its resonant frequency. This is due(p) to the crystals in the glass vibrating together which leads to wizard clear tone. As water is added to the glass, its resonant frequency change s.Resonance is important on a bigger scale than just the use of the Glass Harmonica. It relates to the way structures and other man-made objects oscillate in the outside world. For example, the Takoma Narrows severance Bridge in Washington collapsed due to wind that was gusting at the subscribe resonant frequency of the bridge.6 Further to a greater extent, acoustic resonance is important for instrument builders, as many instruments use resonators, for example, strings on a guitar, the length of a tube and the tension on a drum membrane.Slip-Stick EffectThe slip- wash up phenomenon is define as the spontaneous jerking motion that can occur maculation two objects ar sliding over each other.7 The friction surrounded by two surfaces leads to a stick effect. The stick effect is due to the utilise force not being great enough to overcome the friction. However, as the force employ becomes greater, one of the surfaces begins to slip. When the surface slips, the force applied increa ses the second surfaces velocity. As the velocity increases, the frictional force increases too, until the frictional force is greater than that of the force applied, leading to another stick. The process continues and is named the slip-stick effect.The constant frictional jerking of the finger on the rim of the wine glass causes vibrations within the wall of the glass, leading to the oscillation of the glass and essentially, the tone produced.How does the glass vibrate?The glass begins to vibrate in a very special way when affected by the slip-stick phenomenon. When a moistened finger rubs along the glass, the rim begins oscillating into an elliptical shape due to its relatively elastic nature. Figure 2 portrays an exaggeration of the deformation of the rim of the glass.The rims shape oscillates between the two elliptical shapes shown some(prenominal) hundred times per second, producing an audible tone.HypothesisIn context of the investigation to be undertaken, it is hypothesised that as height of water increases in each of the leash glasses, the frequency produced by each of the glasses will fall. The glass that can contain the greatest volume of water will reduce the to the lowest degree(prenominal) over the course of the test. Additionally, both other glasses will submit a greater rate of frequency decrease. Under test conditions, it is predicted that as the glasses get fuller, the frequency reduction will become greater as the stem of the glass supports the glass, hindering it from vibrating as much.Correlation victimization Frenchs formula, a bilinear relationship can be established between the frequency produced and the height of waterThe harbor has been substituted into the comparability as is built up of a number of constants representing the minginess of liquid, density of glass and glass thickness. Thus, plotting the following as and should present a linear relationshipGraphing the above equation should present a value as gradient.Id eal GraphsIdeally, the graphs should be as depicted belowThe graph on the left depicts the reduction in frequency as height of water increases. The frequency slowly decreases in the first part before speedily diminishing as height increases. The graph on the right has been manipulated using the raw data into a straight-line graph. Its gradient is the value.MethodClear the res publica and prepare the test glass and all other equipment used in experimentation. Place test glass flush on the desk before adopting keep mum in the room. Moisten index finger and begin softly draw the rim of the glass. Continue rubbing the rim of the glass until a standing(a) shake appears. Begin recording dense in the room for a period of 10 seconds. If the standing wave is lost before the end of 10 seconds, stop the recording, delete the recording and repeat the procedure. If the standing wave continues, stop the recording at 10 seconds and stop rubbing the rim of the glass. Open the ANALYSE drop-dow n menu and select PLOT SPECTRUM. Trace along the graph until the peak is reached and record the frequency of the peak. Close the spectrum and delete the recording. relieve 3 times. Measure out 20ml of water in a surgical syringe and add this liquid to the glass. Repeat the method outlined above.The setup of the experiment is pictured belowResultsThe results of the experiment are tabulated below unrefined DataAnalysisFrequency Reduction (Hz)Glass 1Glass 2Glass 3Linear Relationship GraphsGlass 1Glass 2Glass 3-Value for Different Glasses faulting AnalysisThere are terzetto forms of fracture in this experimentStraight line flawMeasurement errorExpected errorStraight Line ErrorMeasurement ErrorMeasurement error can be calculated using the minor(ip)est division of every gear up of equipment used to musical rhythm determine. These are presented belowVernier 0.01mmAudacitys Frequency Spectrum 0.5 HzSyringe Negligible as the volume increments are not factored into the Frenchs form ulaSubstituting sundry(a) values into a rearranged version of Frenchs formula will run into the diverse amounts of measurement error in each trial. The calculations are on tap(predicate) belowFormulaGlass 1Therefore, measurement error is 0.52 HzGlass 2Therefore, measurement error is 0.52 HzGlass 3Therefore, measurement error is 0.52 HzExpected ErrorExpected error can be found by substituting the value for various glasses into the manipulated formula used for the measurement error. The result of graphing this is the expect frequency decrease curve. The graphs are presented belowGlass 1Glass 2Glass 3Average Difference Throughout the Duration of the investigateMaximum DifferenceDiscussionInterpretation of ResultsAccording to the results, the previously theorize hypothesis was proven correct. This is true since the frequency produced by each of the glasses fell as the height of water in each of the three glasses increased. Furthermore, Glass 2, which has the greatest capacity, al so followed suit as it had the least frequency reduction. Moreover, stem of the glass acted as an excellent support for each of the glasses, ensuring that the raw graphed data followed a similar pattern to that anticipate. Another celebrated trend was that the taller glass with the smallest capacity and roentgen had the greatest reduction in frequency. On the other hand, the shortest glass has the most stable and predictable decrease. followers Frenchs formula, justification can be made as to why the values didnt increase as height of glass increased. The values of each of the glasses is made up of the followingWhere the only when variable factors between glasses are , radius of the glass and , thickness of the glass at water level. Thus, as increases, as with Glass 2, the value increases too. Naturally, as decreases, as with Glass 3, the value increases. Glass 3 had a higher value than Glass 1 simply due to the thin nature of the glass. Furthermore, Glass 2 had the highest value due to its monumental radius and almost spherical shape.While it was not a part of this observational investigation at all, it must be noted that the glass with the greatest value produced the loudest sound, that is, the wave with the greatest amplitude. An interesting observation can be made through linking the nature of the glass, the value and the amplitude of the sound wave produced. As the glass becomes slender and rounder, the value increases, which in turn, leads to a louder sound being produced.While the results obtained from the experiment are as were hypothesized, the outcome for the overall investigation is not as straightforward. The varied frequency decrease in the three glasses indicates which would be the most efficient in a Glass Harmonica with limited glasses. The dissimilarity also shows which glass would be able to play a particularised small range more precisely than others. There are distinct advantages/disadvantages regarding high/low frequency reduction. The main advantage of the greater variation in frequency is that one can play a completely range of notes with only a few of the same type of glass. Additionally, the primary disadvantage of a great frequency decrease is that subtle changes in frequency cannot be good made. A method of eliminating this disadvantage is simply using glasses that permit a sulky frequency reduction, such as Glass 2. However, this has its own advantages and disadvantages. The key advantage is that more specific notes in a small range can be played. Nevertheless, a disadvantage of this is that a large number of glasses need to be used, to play each specific note.In the real world, when a Glass Harmonica is used, a whole range of glasses are used due to the fact that more precise notes can be played in a maculation range of frequencies. This is what makes these instruments so expensive. Usually, the higher notes are played using thinner glasses and lower, deeper notes are played using round er, wider glasses.Comparison with Expected ResultsThe results obtained from conducting the data-based investigation are slightly deviant from those expected. It was expected that the values of the various glasses would be ordered the same way as the keeping of frequency, and in the following order, from greatest to smallest frequency retentionThe results obtained are diverging from these and follow the pattern as shown belowHowever, when comparing the data stash away to the expected data, there is a trend on all the graphs as they all begin almost exactly on par with the expected results. Glass 3 had the greatest amount of disagreeence from the expected graph. On average, every frequency measured was 32.25 Hz above or below the value it should have been at. In addition, Glass 2 began on par wuth the expected curve before reducing frequency slightly slower than expected.Nevertheless, the graphs were most consistent in both the beginning and end of each glass. As visible on the al l three of the difference in frequency graphs, the true data began and ended almost exactly oppose to the expected values.While results obtained were fairly accurate, the maximum difference between the expected values and true data in the three glasses was 68.04 Hz.Mistakes, Uncertainties, ErrorsWhile the investigation undertaken does not blatantly show evidence of any epoch-making mistakes/errors, there are certainly a number of anomalies. For example, Glass 3 had a greater value than Glass 1 even though it has a minute radius. The values of the various glasses differ by only a small amount and the reduction of frequency differ by a fairly large amount. Both these must be duly noted.When analysing the raw data, there is a distinct anomalistic middle of all 3 of them. This is a clear indication of a large error caused by either measuring incorrectly each glass was upgrade tested or simple inconsistencies in the peaks of Audacitys frequency spectrum. Regardless, this error in al l 3 experiments caused a deviance from the trendline. Unfortunately, it was not possible to avoid the influence of this error as values had to be calculated using those sections of data.There are a number of errors, caused by the method, which could have influenced the results. Firstly, when measuring the values of height of water and height of glass through the Vernier, there existed a chance of parallax error as the readings may be slightly deviant from the true values. Secondly, increasing volume of water instead of height of water for ease of measurement may not have had the correct effect and it may have been easier to simply measure heights in standard increments. Lastly, the standing wave may have broken at points, leading to the peaks of the frequency spectrum having an effect on the rigor of the results, for example, the raw data and its difference to the expected data wou